Security and efficiency are the main concerns when designing an authenticated key agreement protocol. In 2005, Choie et al. proposed two identity-based authenticated key agreement protocols based on bilinear pairings. In this paper, however, we point out that both their two protocols are of certain security or efficiency problems. For their first protocol, we show that it is vulnerable to a signature forgery attack which undermines its key integrity and then suggest a simple method to solve the problem. As for their second protocol, we discover much computational redundancy and then put forward a more efficient modified protocol which discards the unnecessary computations.
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